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Friday, September 7, 2012

Two-Way ANOVA Interactions in SPSS

Typically, when conducting an ANOVA, we can get the pairwise
comparison results for the differences between the groups on the dependent
variable. However, when we step it up to two grouping variables, SPSS tends to
not give us this option.

For
example, let’s say you wanted to test for difference in “Test Scores” by gender
(male vs. female) and by ethnicity (white vs. black vs. Hispanic). In the Options… dialogue box in SPSS, you can
move over Gender, Ethnicity, and Gender*Ethnicity. This will give the marginal
means and standard errors for each of the groups. However, if you select the
box “Compare main effects”, you will only get comparisons by Gender and by
Ethnicity, not by the combination. The secret to getting the main effects comparison is in
examining the syntax. So first “Paste” the analysis into a Syntax file. It
should look something like what is below:

UNIANOVA TestScores BY Gender Ethnicity

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/EMMEANS=TABLES(Gender) COMPARE

/EMMEANS=TABLES(Ethnicity) COMPARE

/EMMEANS=TABLES(Gender*Ethnicity)

/CRITERIA=ALPHA(.05)

/DESIGN=Gender
Ethnicity Gender*Ethnicity.

From the
above you can see that SPSS did not add the “COMPARE” syntax to the
Gender*Ethnicity means. In order to conduct the comparisons, we have to
manually add it. However, simply adding “COMPARE” is not enough. Because it is
an interaction, you have to specify what you want to compare. So it should be
changed into what is below:

UNIANOVA TestScores BY Gender Ethnicity

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/EMMEANS=TABLES(Gender) COMPARE

/EMMEANS=TABLES(Ethnicity) COMPARE

/EMMEANS=TABLES(Gender*Ethnicity) COMPARE (Gender)

/CRITERIA=ALPHA(.05)

/DESIGN=Gender
Ethnicity Gender*Ethnicity.

What this
will do is it will compare the Test Scores by gender for each ethnicity
separately. But what about comparing the ethnicity for each gender? That
simply requires another line in the syntax, which is below. However, conducting
all these pairwise comparisons is going to affect Type I error. We may have
some significant differences there that may be only significant due to random
chance. In order to adjust for Type I error, we can include the Bonferroni
adjustment the the comparisons. So the final syntax below has both two-way
interactions examined with a Bonferonni adjustment added onto the p-values to adjust for Type I error.

UNIANOVA TestScores BY Gender Ethnicity

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/EMMEANS=TABLES(Gender) COMPARE ADJ(BONFERRONI)

/EMMEANS=TABLES(Ethnicity) COMPARE ADJ(BONFERRONI)

/EMMEANS=TABLES(Gender*Ethnicity) COMPARE (Gender) ADJ(BONFERRONI)

/EMMEANS=TABLES(Gender*Ethnicity) COMPARE (Ethnicity) ADJ(BONFERRONI)

/CRITERIA=ALPHA(.05)

/DESIGN=Gender
Ethnicity Gender*Ethnicity.

To make
things visual, you can make a bar chart using the estimated marginal means so
you might have something like the chart below.